In this brief, continuous-time nonlinear systems with extended matching uncertainties are considered. The problem of designing a state-feedback adaptive learning control of reduced complexity — just including a single adaptive learning estimation scheme in the upper subsystem and a high-gain proportional action in the input channel — is addressed. By properly setting the control parameters, exponential output tracking of (sufficiently smooth) periodic reference signals with a known period is achieved. Fourier series expansions are used and estimates of the resulting Fourier coefficients are continuously adapted based on the persistency of excitation conditions that naturally hold due to the orthogonal nature of the sinusoidal basis functions.

在此简介中，考虑了具有扩展匹配不确定性的连续时间非线性系统。解决了设计复杂性降低的状态反馈自适应学习控制的问题——仅包括上层子系统中的单个自适应学习估计方案和输入通道中的高增益比例动作。通过适当设置控制参数，可以实现对已知周期的（足够平滑的）周期性参考信号的指数输出跟踪。使用傅立叶级数展开，并根据由于正弦基函数的正交性质而自然保持的激发条件的持久性，不断调整所得傅立叶系数的估计值。